He's been gunning for you ever since you embarrassed him at the party.

To practice fowling or hunting small game; chiefly in participial form: to go gunning.

Origin

Middle English Lady Gunilda which was a huge crossbow that used powerful shot. It later became used for firearms like cannons and muskets. The Germanic woman’s name “Gundahild” , cognate to modern Scandinavian Gunhild, means “war" + "battle maid”.